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I don't blame shippers for not wanting to navigate the strait. If they lose a ship they are out-of-commission for the better part of a decade while a replacement is built.
Not to mention the civilian crew who did not sign up for this shit.
You can't just go down to the barge store and walk out carrying a new superfreighter.
That's bad enough for that business, but enough of those will have a significant impact on the global economy. Supply goes down, prices go up, customers suffer.
Of course, so would not navigating the strait. But that's the point. They don't even have to mine it, they could be bluffing, but even the possibility is just not worth it to the operators of those ships.